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Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
We consider a pair of collectively oscillating networks of dynamical elements and optimize their internetwork coupling for efficient mutual synchronization based on the phase reduction theory developed in Ref. [H. Nakao, S. Yasui, M. Ota,…
We study sparse principal component analysis in the high-dimensional, sample-limited regime, aiming to recover a leading component supported on a few coordinates. Despite extensive progress, most methods and analyses are tailored to the…
We introduce and study systems of randomly coupled maps (RCM) where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally…
This paper presents new results and reinterpretation of existing conditions for strong structural controllability in a structured network determined by the zero/non-zero patterns of edges. For diffusively-coupled networks with self-loops,…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…
A key challenge in systems biology is the elucidation of the underlying principles, or fundamental laws, which determine the cellular phenotype. Understanding how these fundamental principles are altered in diseases like cancer is important…
We propose a practical approximation to the exchange-correlation functional of (time-dependent) density functional theory for many-electron systems coupled to photons. The (time non-local) optimized effective potential (OEP) equation for…
The constituents of a complex system exchange information to function properly. Their signalling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange…
Interacting random field of probabilities links Kolmogorov law 0-1 and Bayesian probabilities observing Markov diffusion process under Yes-No actions of random impulse. These objective probabilities measure virtual probing impulses…
We study a system of coupled pendula with diffusive interactions, which could depend both on positions and on momenta. The coupling structure is defined by an undirected network, while the dynamic equations are derived from a Hamiltonian;…
In quantum networks multipath entanglement purification (MEP) between a pair of source-destination nodes can substantially strengthen their entanglement connection. An efficient MEP strategy can therefore increase the size of the network…
We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense (average degree…
In this paper, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modelled using the nearest neighbor…
Sampling considerations limit the experimental conditions under which information theoretic analyses of neurophysiological data yield reliable results. We develop a procedure for computing the full temporal entropy and information of…
A neural network works as an associative memory device if it has large storage capacity and the quality of the retrieval is good enough. The learning and attractor abilities of the network both can be measured by the mutual information…
This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing and…
We study the limiting behavior of interacting particle systems indexed by large sparse graphs, which evolve either according to a discrete time Markov chain or a diffusion, in which particles interact directly only with their nearest…
Complex dynamical systems are prevalent in various domains, but their analysis and prediction are hindered by their high dimensionality and nonlinearity. Dimensionality reduction techniques can simplify the system dynamics by reducing the…